1. Field of the Invention
The present invention relates generally to code word selection and, in particular, to a code word selection method in a wireless communication system.
2. Description of the Related Art
In order to facilitate the spatial multiplexing of wireless Multiple-Input-Multiple-Output (MIMO) systems is essential for a transmitter to have Channel-State Information (CSI) corresponding to the transmitter and a receiver. Limited feedback schemes using codebooks are commonly used by receivers as methods for sending CSI to transmitters in Frequency-Division-Duplex (FDD) systems.
There are various codebook schemes that attempt to efficiently represent CSI under certain assumed channel characteristics. For example, Grassmannian-Line-Packing (GLP) codebooks, Discrete-Fourier-transformation (DFT) codebooks, and block-diagonalization codebooks are suitable for Independent, Identically Distributed (i.i.d) Rayleigh channels, spatially correlated channels, and dual-polarized channels respectively.
All of the above-described codebooks are fixed codebooks (i.e., codebooks that are not changed or updated with changes in time or frequency). In the Institute of Electrical and Electronics Engineers (IEEE) 802.16m specification, however, includes two kinds of codebook adaptation methods. A transformation (Adaptive) codebook corresponds to an adaptation method for spatially correlated channels and a differential codebook is used for temporally correlated channels.
Among various kinds of differential codebooks, a polar-cap differential codebook has been adopted in the IEEE 802.16m specification.
FIG. 1 is a diagram illustrating operations of a polar-cap differential codebook.
Referring to FIG. 1, a polar-cap differential codebook is rotated to a previously selected codeword, and a new codebook is formed for a next time instant. If there is a strong temporal correlation in a channel, the channel at time i may be close to the channel at time τ-1. The polar-cap differential codebook tries to utilize this temporal correlation of the channel. There is a pre-defined polar-cap differential codebook {tilde over (W)}τ={{tilde over (w)}1τ . . . , {tilde over (w)}2Bτ} for each time τ (or the differential codebook can be fixed for all τ for simplicity) and all the codewords in the polar-cap codebook are rotated by a rotation matrix, which is a function of the previously selected codeword (or pre-coding matrix) and the basis of {tilde over (W)}τ. By updating codewords (or pre-coding matrices) for pre-coding, the same number of codewords (or pre-coding matrices) can be assigned to a smaller region, which results in less channel quantization error while maintaining the same feedback overhead.
For the future wireless communication systems such as 3rd Generation Partnership Project (3GPP) Long Term Evolution (LTE) or LTE-Advanced systems, Dual-Polarized (DP) antennas, especially Rotated-Dual-Polarized (RDP) antennas, rather than Uniform-Linear-Array (ULA) antennas, have been considered for baseline scenarios.
FIG. 2 is a diagram illustrating Multiple Input Single Output (MISO) antenna scenarios.
Referring to FIG. 2, FIG. 2(a) shows a DP MISO antenna scenario, while FIG. 2(b) shows an RDP MISO antenna scenario. In the DP MISO scenario, there is power imbalance between the horizontal transmit antenna and the vertical receive antenna, such that the channel vector hDP can be defined according to Equation 1 as follows:hDP=[h1 h2 √{square root over (XDP)}h3 √{square root over (XDP)}h4]  (1)
Equation 1 is applied to a four-transmission (4Tx) antenna case where hi is an i.i.d. complex Gaussian random variable with zero mean and unit variance representing channel gain from an i-th transmit antenna to a receive antenna, and XDP is the inverse of an XPD value representing cross-polar discrimination in a DP scenario. The parameter 0≦χ≦1 where 1≦XPD≦∞. The XPD refers to the physical ability of the antennas to distinguish the orthogonal polarization. In the RDP MISO scenario, however, the impact of XPD for power imbalance is not severe as DP case because XPD impacts all channel elements in the RDP MISO scenario. In the RDP MISO scenario, the channel vector can be defined according to Equation 2 as follows:hRDP=[√{square root over (XRDP)}h1 √{square root over (XRDP)}h2 √{square root over (XRDP)}h3 √{square root over (XRDP)}h4].   (2)
Even in the DP MISO or MIMO scenarios, the impact of XPD decreases if multipath fading occurs. In such an environment, codewords (or pre-coding matrices) that have Rotated-Block-Diagonal (RBD) structures are beneficial. A 4×1 vector wk has an RBD structure, when wk is defined according to Equation 3 as follows:
                                                        G                              -                1                                      ⁢                          w              k                                =                      [                                                            a                                                                              b                                                                              0                                                                              0                                                      ]                          ⁢                                  ⁢                  or          ⁢                                          [                                                    0                                                                    0                                                                    a                                                                    b                                              ]                                    (        3        )            In Equation 3, G is a Givens rotation matrix, and a and b are complex numbers. With respect to a 45° tilted 4Tx antenna, G is expressed according to Equation 4 as follows:
                                                        G              =                            ⁢                              [                                                                                                    cos                        ⁡                                                  (                                                      45                            ⁢                            °                                                    )                                                                                                            0                                                                                      -                                                  sin                          ⁡                                                      (                                                          45                              ⁢                              °                                                        )                                                                                                                                      0                                                                                                  0                                                                                      cos                        ⁡                                                  (                                                      45                            ⁢                            °                                                    )                                                                                                            0                                                                                      -                                                  sin                          ⁡                                                      (                                                          45                              ⁢                              °                                                        )                                                                                                                                                                                                  sin                        ⁡                                                  (                                                      45                            ⁢                            °                                                    )                                                                                                            0                                                                                      cos                        ⁡                                                  (                                                      45                            ⁢                            °                                                    )                                                                                                            0                                                                                                  0                                                                                      sin                        ⁡                                                  (                                                      45                            ⁢                            °                                                    )                                                                                                            0                                                                                      cos                        ⁡                                                  (                                                      45                            ⁢                            °                                                    )                                                                                                                    ]                                                                                        =                            ⁢                                                [                                                                                                              1                                                      2                                                                                                                      0                                                                                              -                                                      1                                                          2                                                                                                                                                  0                                                                                                            0                                                                                              1                                                      2                                                                                                                      0                                                                                              -                                                      1                                                          2                                                                                                                                                                                                                    1                                                      2                                                                                                                      0                                                                                              1                                                      2                                                                                                                      0                                                                                                            0                                                                                              1                                                      2                                                                                                                      0                                                                                              1                                                      2                                                                                                                                ]                                .                                                                        (        4        )            
As shown in Table 1, below, there are sixteen codewords (or pre-coding matrices) in LTE rank one codebook, and eight codewords (or pre-coding matrices) in the LTE rank one codebook have an RBD structure. As shown in Table 1, codewords (or pre-coding matrices) k=1, 2, 3, 4, 9, 10, 11 and 12 have an RBD structure.
TABLE 1LTE rank 1 codewords and their rotated elementsCodebook index kLTE rank 1 codebook wkG−1wk1            1      2        ⁡          [                                    1                                1                                1                                1                              ]        T            1              2              ⁡          [                                    1                                1                                0                                0                              ]        T 2            1      2        ⁡          [                                    1                                j                                              -              1                                                          -              j                                          ]        T            1              2              ⁡          [                                    0                                0                                              -              1                                                          -              j                                          ]        T 3            1      2        ⁡          [                                    1                                              -              1                                            1                                              -              1                                          ]        T            1              2              ⁡          [                                    1                                              -              1                                            0                                0                              ]        T 4            1      2        ⁡          [                                    1                                              -              j                                                          -              1                                            j                              ]        T            1              2              ⁡          [                                    0                                0                                              -              1                                            j                              ]        T 5            1      2        ⁡          [                                    1                                                              1                +                j                                            2                                                          j                                                                                -                  1                                +                j                                            2                                                        ]        T            1              2              ⁡          [                                                                  1                +                j                            2                                                          j                              2                                                                                                          -                  1                                +                j                            2                                                                          -                1                                            2                                                        ]        T 6            1      2        ⁡          [                                    1                                                                                -                  1                                +                j                                            2                                                                        -              j                                                                          1                +                j                                            2                                                        ]        T            1              2              ⁡          [                                                                  1                -                j                            2                                                          j                              2                                                                                                          -                  1                                -                j                            2                                                          1                              2                                                        ]        T 7            1      2        ⁡          [                                    1                                                                                -                  1                                -                j                                            2                                                          j                                                              1                -                j                                            2                                                        ]        T            1              2              ⁡          [                                                                  1                +                j                            2                                                                          -                j                                            2                                                                                                          -                  1                                +                j                            2                                                          1                              2                                                        ]        T 8            1      2        ⁡          [                                    1                                                              1                -                j                                            2                                                                        -              j                                                                                            -                  1                                -                j                                            2                                                        ]        T            1              2              ⁡          [                                                                  1                -                j                            2                                                                          -                j                                            2                                                                                                          -                  1                                -                j                            2                                                                          -                1                                            2                                                        ]        T 9            1      2        ⁡          [                                    1                                1                                              -              1                                                          -              1                                          ]        T            1              2              ⁡          [                                    0                                0                                              -              1                                                          -              1                                          ]        T 10            1      2        ⁡          [                                    1                                j                                1                                j                              ]        T            1              2              ⁡          [                                    1                                j                                0                                0                              ]        T 11            1      2        ⁡          [                                    1                                              -              1                                                          -              1                                            1                              ]        T            1              2              ⁡          [                                    0                                0                                              -              1                                            1                              ]        T 12            1      2        ⁡          [                                    1                                              -              j                                            1                                              -              j                                          ]        T            1              2              ⁡          [                                    1                                              -              j                                            0                                0                              ]        T 13            1      2        ⁡          [                                    1                                1                                1                                              -              1                                          ]        T            1              2              ⁡          [                                    1                                0                                0                                              -              1                                          ]        T 14            1      2        ⁡          [                                    1                                1                                              -              1                                            1                              ]        T            1              2              ⁡          [                                    0                                1                                              -              1                                            0                              ]        T 15            1      2        ⁡          [                                    1                                              -              1                                            1                                1                              ]        T            1              2              ⁡          [                                    1                                0                                0                                1                              ]        T 16            1      2        ⁡          [                                    1                                              -              1                                                          -              1                                                          -              1                                          ]        T            1              2              ⁡          [                                    0                                              -              1                                                          -              1                                            0                              ]        T
Conventional codebook design is not optimized for Rotated Dual Polarized (RDP) antenna conditions. Accordingly, there is a need for codebook designs that are optimized for RDP antenna conditions.